MULTIPLE SOLUTIONS FOR A DIRICHLET PROBLEM WITH p-LAPLACIAN AND SET-VALUED NONLINEARITY

DOI10.1017/S0004972708000282zbMath1147.35025OpenAlexW1972482645MaRDI QIDQ3514864

Motreanu, Dumitru, Diego Averna, Salvatore A. Marano

Publication date: 23 July 2008

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972708000282

zbMATH Keywords

critical points\(p\)-Laplaciansub- and supersolutionsgeneralized gradientmultiple nontrivial solutions

Mathematics Subject Classification ID

Variational inequalities (49J40) Nonlinear boundary value problems for linear elliptic equations (35J65) Variational methods for second-order elliptic equations (35J20)

Related Items (12)

On a Robin problem with \(p\)-Laplacian and reaction bounded only from above ⋮ Positive, Negative, and Nodal Solutions to Elliptic Differential Inclusions Depending on a Parameter ⋮ ON A DIRICHLET PROBLEM WITH p-LAPLACIAN AND SET-VALUED NONLINEARITY ⋮ Sign-changing solutions for nonlinear elliptic problems depending on parameters ⋮ Unnamed Item ⋮ Multiple solution results for elliptic Neumann problems involving set-valued nonlinearities ⋮ Multiple solutions for nonlinear coercive problems with a nonhomogeneous differential operator and a nonsmooth potential ⋮ Constant sign and sign changing solutions for systems of quasilinear elliptic equations ⋮ Qualitative analysis of solutions of obstacle elliptic inclusion problem with fractional Laplacian ⋮ General comparison principle for quasilinear elliptic inclusions ⋮ Constant sign and nodal solutions for problems with the \(p\)-Laplacian and a nonsmooth potential using variational techniques ⋮ Multiple solutions to elliptic inclusions via critical point theory on closed convex sets

Cites Work

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• A version of Zhong's coercivity result for a general class of nonsmooth functionals
• Morse theory for continuous functionals
• The beginning of the Fučik spectrum for the \(p\)-Laplacian
• Multiple solutions for a class of elliptic hemivariational inequalities
• Constant-sign and sign-changing solutions for nonlinear eigenvalue problems
• On some elliptic hemivariational and variational-hemivariational inequalities
• On a class of nonlinear dirichlet problems with multiple solutions
• Sharp nonuniqueness results for some nonlinear problems
• A multiplicity theorem for problems with the \(p\)-Laplacian

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